Representation of self-similar Gaussian processes

2014/01/14 by Adil Yazigi, Yazigi, Adil
Computer Science · Physics and Astronomy · #60G15 #60G18 #60G22 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Probability (math.PR) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1401.3236

openalex publication_date 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the canonical Volterra representation for a self-similar Gaussian process by using the Lamperti transformation of the corresponding stationary Gaussian process, where this latter one admits a canonical integral representation under the assumption of pure non-determinism. We apply the representation obtained for the self-similar Gaussian process to derive an expression for Gaussian processes that are equivalent in law to the self-similar Gaussian process in question.

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